Honors Advanced Algebra with Trigonometry
Probability
Target Goals
By the end of this chapter, you should be able to…

Solve problems using the Counting Principle. (Day 1)
_____ got it
_____needs work
_____ no clue

Solve problems involving permutations. (Day 2)
_____ got it
_____needs work
_____ no clue
Solve problems involving combinations. (Day 3)
_____ got it
_____needs work
_____ no clue


Find the probability of an event and determine the odds of success or failure. (Day 4)
_____ got it
_____needs work
_____ no clue

Find the probability of two or more independent or dependent events. (Day 5)
_____ got it
_____needs work
_____ no clue

Find the probability of mutually exclusive events or inclusive events. (Day 6)
_____ got it
_____needs work
_____ no clue
Honors Advanced Algebra with Trigonometry
Assignment Guide
Probability
The Counting Principle
Target Goal: Solve problems using the Counting Principle.
.
HW #1
Worksheet
Linear Permutations
Target Goal: Solve problems involving permutations.
HW #2
Worksheet
Combinations
Target Goal: Solve problems involving combinations.
HW #3
Worksheet
Day 1 – Day 3 Review
HW #3.5
Worksheet
Probability
Target Goal: Find the probability of an event and determine the odds of success or failure.
HW #4
Worksheet
QUIZ Day 1 – Day 3
Multiplying Probabilities
Target Goal: Find the probability of two or more independent or dependent events.
HW #5
Worksheet
Adding Probabilities
Target Goal: Find the probability of mutually exclusive events or inclusive events.
HW #6
Worksheet
QUIZ Day 4 – Day 5
Probability Review
HW #7
Worksheet
Tentative Test Date: _______________________
Honors Advanced Algebra with Trigonometry
The Counting Principle
Probability Notes (Day 1)
Name: _____________________
Date: ______________________
Period: ____________________
Target Goal: Solve problems using the Counting Principle.
Kevin wants to buy a new car. He has already chosen the make and model, but still must decide between
automatic or manual transmission, a sunroof or no sunroof, and a color (red, white, or black). These decisions
are all called INDEPENDENT EVENTS because one decision will not affect the other. We can use a tree
diagram to illustrate all of the choices that Kevin still must make:
Now we can see that Kevin has 12 choices to choose from. We could list these choices in a SAMPLE SPACE:
The total number of choices can also be found without drawing a diagram:
This application is an example of the BASIC COUNTING PRINCIPLE which states the following:
Suppose an event can occur in p different ways; another event can occur in q different ways, then there
are p  q ways both events can occur.
Ex 1: How many 4-letter patterns can be formed using the letters u, v, w, x, y, and z if the letters may be
repeated?
But what if the letters in the example above cannot repeat? This would be a DEPENDENT EVENT because
the number of choices for one event does affect other events.
Ex 2: How many 4-letter patterns can be formed using the letters u, v, w, x, y, and z if letters may not be
repeated?
Practice:
1. Tell whether the events are independent or dependent, then solve.
a. How many 2-digit numbers can be formed from 1, 2, 3, 4, and 5, if repetitions are allowed?
b. How many ways can 5 different books be arranged on a shelf?
c. How many seven-digit numbers can be formed from the digits 0 - 9 if each digit can be used more
than once?
d. From the letters a, e, i, o, r, m, and n, how many different four letter patterns can be formed if no
letter occurs more than once?
2. From 1d above, how many of these patterns begin with a vowel and end with a consonant?
3. List the possible outcomes if you flip a coin three times. What is this list called?
4. How many ways can 5 cars be parked along the street if the only SUV must be in the middle?
5. How many ways can six books be arranged on a shelf if one of the books is a dictionary and it must be
on an end?
6. Using the letters from the word equality, how many four letter patterns can be formed in which q is followed
immediately by u?
7. Draw a chart to represent the sample space of possible outcomes for rolling two dice.
Assignment #1: Worksheet
Honors Advanced Algebra with Trigonometry
The Counting Principle
Assignment #1
Name: _____________________
Date: ______________________
Period: ____________________
Solve each problem.
1. The letters g, h, j, k, and l are to be used to form 5-letter passwords for an office security system. How
many passwords can be formed if the letters can be used more than once in any password?
2. A store has 15 sofas, 12 lamps, and 10 tables at half price. How many different combinations of a sofa, a
lamp, and a table can be sold at half price?
Draw a tree diagram to illustrate all the possibilities.
3. the possibilities for boys and girls
in a family with two children
4.
the possibilities for boys and girls
in a family with three children
Solve each problem.
5. A license plate must have two letters (not I or O) followed by three digits. The last digit cannot be zero.
How many possible plates are there?
6. There are five roads from Albany to Briscoe, six from Briscoe to Chadwick, and three from Chadwick to
Dover. How many different routes are there from Albany to Dover via Briscoe and Chadwick?
7. For a particular model of car, a car dealer offers 6 versions of that model, 18 body colors, and 7 upholstery
colors. How many different possibilities are available for that model?
8. How many ways can six different books be arranged on a shelf?
9. Three different colored six-sided dice are tossed. How may distinct outcomes can occur?
10. How many ways can six books be arranged on a shelf if one of the books is a dictionary and it must be on
an end?
11. Using the letters from the word equation, how many 5-letter patterns can be formed in which q is followed
immediately by u?
12. Consider the letters a, e, i, o, r, s, and t.
a. How many different 4-letter patterns can be formed from these letters if no letter occurs more
than once?
b. How many of these patterns begin with a vowel and end with a consonant?
13. How many 5-digit numbers exist between 65,000 and 69,999 if no digit is to be repeated in each number?
14. A Chinese restaurant offers a special price for customers who dine before 6:30 p.m. This offer includes an
appetizer, a soup, and an entrée all for $6.95. There are 4 choices of appetizers, 3 soups, and 5 entrées.
How many different meals are available under this offer?
15. Four ferry boats run round trips between Harrod and Lafayette.
a. How many different ways can a traveler make a round trip?
b. How many different ways can a traveler make a round trip, by riding a different ferry on
the return trip?
Honors Advanced Algebra with Trigonometry
Linear Permutations
Probability Notes (Day 2)
Name: _____________________
Date: ______________________
Period: ____________________
Warm-Up:
1. Suppose Moe picks a number from 1 to 4, Larry picks a number from 5 to 7, and Curly picks the
number 8 or 9. How many sets of three numbers are possible? Write the sample space for at least 6
possibilities followed by ”…”.
2. How many different three-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6, and 7 if no digit is
used twice?
3. Superstitious Sandy, the coach of a baseball team, starts the same nine players in every game but arranges
them in a different batting order each time. How many games must the team play in order for Sandy to use
all possible batting orders?
4. Goo Lash Caterers provided a seven-course dinner for a party. Unfortunately, they forgot to label the
containers of food, so the courses had to be served in random order. In how many different orders could the
courses have been served?
_________________________________________________________________________________________
Target Goal: Solve problems using permutations.
In some of the problems above, we multiply a number by every number below it. This is called a
FACTORIAL; we use an exclamation mark to signify a factorial.
exs.
To find the factorial of a positive integer by graphing calculator:
1. enter the number you are trying to find the factorial of
2. MENU, PRB, 4: !, ENTER
In warm-up problem #1, order is not important. Larry, Moe, and Curly can choose their numbers in any order,
that is, they are independent events. In the other four problems, however, order is important. That is, the
selection of the second event depends on the first event. When ORDER MATTERS, we call these problems
PERMUTATIONS. A linear permutation is the arrangement of objects in a certain linear order.
Definition of P(n, r) – the number of permutations of n objects taken r at a time is defined as follows:
To find the number of permutations of n objects by graphing calculator:
1. enter n number of objects
2. MATH, PRB, 2: nPr
3. enter r number of objects taken at a time
Ex 1: How many ways can 3 books be placed on a shelf if chosen from 8 different books?
Ex 2: From a committee of 18 people, how many ways can a president, vice-president, and treasurer be
assigned?
Ex 3: How many different 4-digit garage codes can be made if there are no repeats permitted?
Permutations with repetitions – the number of permutations of n objects of which p are alike and q are alike is:
Ex 4: There are 3 identical white flags and 5 identical blue flags that are used to send signals. All 8 are to be
arranged in a row. How many signals can be given?
Directions: Determine which scenario has repeats and which does not, then choose the appropriate way
to solve each.
Ex5: How many ways can the letters from the following words be arranged?
a. FAREWELL
b. ILLINI
c. COLLECTION
Ex6:. How many ways can 2 different geometry, 4 different geography, 5 different history, and 3 different
physics books be arranged on a shelf by subject?
Ex7:
How many ways can 2 geometry, 4 geography, 5 history, and 3 physics books be arranged on a shelf
(not by subject) if all books within a subject are indistinguishable?
Ex8: How many ways can the digits from 755,232 be arranged?
Ex9: We have a group of gems to design a bracelet, including 7 emeralds, 4 rubies, and 3 diamonds.
a. How many different bracelet designs are possible if each gem is unique?
b. How many different bracelet designs are possible if each type of gem is indistinguishable?
Ex10: Determine whether the warm-up problems are dependent or independent, then rework the dependent
problems in terms of a permutation.
Assignment #2: Worksheet
Honors Advanced Algebra with Trigonometry
Linear Permutations
Assignment #2
Name: _____________________
Date: ______________________
Period: ____________________
Review the basic counting principle by completing the following problems.
1. A box contains 20 muffins, 5 of which are blueberry and the rest of which are raisin. In how many ways
can a person choose 2 blueberry muffins and 3 raisin muffins if the first choice must be a raisin muffin and
the two kinds must be chosen alternately?
2. The Thirty-Seven Flavors ice cream shop offers 37 different kinds of ice cream. How many different
2-scoop cones can be ordered if customers are given a choice of plain or sugar cones also? (Assume that the
customers asking for two different flavors can specify the order in which the flavors are put on the cone.)
Show how the following problems can be completed using (a) the basic counting principle and
(b) permutations.
3. How many different four-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6, 7, and 8 if no
digit is used twice?
a.
b.
4. In how many orders can the numbers 11, 22, 33, 55, 88, 99, and 101 be listed?
a.
b.
5. How many batting orders can a coach make of 9 players from a roster of 12 players?
a.
b.
6. Radio station WOLD plays ten requests between 10:00 and 11:00. In how many different orders can each
group of ten songs be played?
a.
b.
How many different ways can the letters of each word be arranged?
7. SEE
8. LEVEL
9. ALASKA
10. PERPENDICULAR
Solve each problem. Be sure to consider repeats when applicable.
11. Don has 5 pennies, 3 nickels, and 4 dimes. The coins of each denomination are indistinguishable.
How many ways can he arrange the coins in a row?
12. How many 6-digit numbers can be made using the digits from 833,284?
13. How many ways can 4 nickels and 5 dimes be distributed among 9 children if each is to receive one coin?
14. Madame Estelle designs jewelry. She is designing a bracelet that will contain a gem in each link of the
bracelet. She has 8 emeralds, 5 rubies, and 3 diamonds. The gem in each type of stone are
indistinguishable from one another. How many different bracelet designs are possible?
Write the sample space for the following problem.
15. Monica, Rachel, and Phoebe like to compete for first, second, and third place in their math class. Write the
sample space for possible lineups.
Honors Advanced Algebra with Trigonometry
Combinations
Probability Notes (Day 3)
Name: _____________________
Date: ______________________
Period: ____________________
Warm-Up:
1. How many different ways can the letters of PARALLEL be arranged?
2. How many different 3-digit numbers can be arranged from the digits 5, 6, 7, 8, or 9…
a. if digits may repeat?
b. if digits may not repeat?
3. Which part from #3 represents a permutation? Why? Solve using this idea.
4. From a team of 16, how many different batting orders of 9 can be written?
5. Five mystery and four romance novels are to be arranged on a shelf. How many ways can they be arranged
if all the mystery books must be together?
_________________________________________________________________________________________
Target Goal: Solve problems involving combinations..
Yesterday, we focused on permutations which were dependent systems where the order was important. In #5
above, for example, the order is important and thus it is a permuatation. What if the problem asked how may
different teams of nine can be chosen (instead of “lined up”)? Notice here that the order is not important. This
is called a COMBINATION.
Determine whether the following are permutations or combinations:
a. How many committees of three can represent our class?
b. How many ways can we assign a president first, vice president second, etc. to that committee.
c. How many rummy hands of 7 cards exist?
d. Placing 8 books on a shelf.
e. Making a classroom seating chart.
f. Finding the number of diagonals of a polygon.
Definition of C(n,r) – the number of combinations of n distinct objects taken r at a time is defined as
To find the number of combinations of n objects by graphing calculator:
1. enter n number of objects
2. MATH, PRB, 3: nCr
3. Enter r number of objects taken at a time
Examples:
1. How many committees of 5 students can be selected from a class of 25?
2. A box contains 12 black and 8 green marbles. How many ways can 3 black and 2 green marbles be chosen?
3. Given 7 distinct points in a plane, how many line segments will be drawn if every pair of points is
connected?
4. How many different 13-card bridge hands can be dealt from a standard deck of 52 cards?
5. From a deck of 52 cards, how many 5 card hands can be selected to meet the following conditions?
a.
hand has exactly 3 aces
b.
hand has at least 3 aces
Assignment #3: Worksheet
Honors Advanced Algebra with Trigonometry
Combinations
Assignment #3
Name: _____________________
Date: ______________________
Period: ____________________
Determine whether each situation involves a permutation or a combination.
1. a hand of 5 cards from a deck of cards
2. matching the answers on a true/false test
3. putting students in assigned seats
4. a 2-man, 2-woman subcommittee of the Campaign Funds committee that has 8 men and 7 women
Solve each problem.
5. You are required to read 5 books from a list of 12 great American novels. How many different groups can
be selected?
6. There are 85 telephones in the editorial department of ‘TEEN magazine. How many 2-way connections can
be made among the office phones?
7. There are 27 people in an Algebra class, but only 25 computers in the computer lab, so each student must
take turns going to the lab. How many different groups of 25 can the teacher send to the lab?
8. From a deck of 52 cards, how many 7 card hands can be selected with exactly 2 aces?
9. From a deck of 52 cards, how many 7 card hands can be selected with at least 3 aces?
A bag contains 9 blue, 4 red, and 6 white chips. How many ways can 5 chips be selected to meet each
condition?
10. all blue
11. all red
12. 2 red and 3 blue
From a group of 8 juniors and 10 seniors, a committee of 5 is to be formed to discuss plans for the spring
dance. How many committees can be formed given each condition?
13. 3 juniors and 2 seniors
14. all seniors
Honors Advanced Algebra with Trigonometry
Permutations and Combinations
Assignment #3.5
Name: _____________________
Date: ______________________
Period: ____________________
Use the basic counting principle, permutations or combinations to complete the following problems.
1. To create an entry code, you must first choose 3 letters and then 5 single-digit numbers.
a. How many entry codes can you create if the letters and digits can repeat?
b. How many entry codes can you create if the letters and digits cannot repeat?
2. In a race of twenty people, how many different ways can the first three runners arrive at the finish line?
3. In how many orders can you read nine books out of thirteen in your room?
4. How many groups of four books can be selected from the thirteen in your room?
5. How many ways can the letters in the word LINEAR be arranged?
6. How many ways can the letters in the word PARALLELOGRAM be arranged?
7. Kathy has 4 pennies, 5 nickels, and 6 dimes. The coins of each denomination are indistinguishable. How
many ways can she arrange the coins in a row?
8.
How many ways can 3 identical pens and 4 identical pencils be distributed among 7 student if each is to
receive one writing utensil?
9. How many groups of five students can be selected to represent our class of thirty students?
10. How many ways can the top five students place (highest grade, next highest…5th highest) out of the thirty in
our class?
11. A bag contains 8 blue, 7 red, and 10 white chips. How many ways can 6 chips be selected to meet each
condition?
a. all blue
b. all red
c.
2 blue and 4 red
12. How many different shirts can you get from a store that has three styles in seven colors and four sizes?
13. A box contains 12 donuts, 4 of which are vanilla covered and 8 of which are chocolate covered. How many
groups of 2 vanilla covered and 3 chocolate covered donuts can be chosen from the box?
14. Jessica was asked to choose five paintings from a collection of eight and hang them on the wall in a row.
How many different ways could the wall be decorated?
Honors Advanced Algebra with Trigonometry
Probability
Probability Notes (Day 4)
Name: _____________________
Date: ______________________
Period: ____________________
Warm-Up:
1. Combination or permutation?
a. A committee of seven members from the U.S. Senate.
b. Lining up in a cafeteria line.
c. A sergeant selecting 6 “volunteers” for a special duty.
d. Awarding first, second, and third prize to eight horses competing in a race.
2. Consider whether the problem is a counting problem, permutation, permutation with repeats, or
combination, and then solve.
a. How many three-digit numbers can be formed from 1, 2, 3, 4, 5, if digits may repeat?
b. How many three-digit numbers can be formed from 1, 2, 3, 4, 5, if digits may not repeat?
c. How many ways can the digits from the number 12,334,556 be arranged?
d. Pete’s Pizza Parlor offers ten pizza toppings. Pete’s special includes a choice of any three toppings.
How many three-topping pizzas can be ordered?
e. A box contains 20 muffins, 5 of which are blueberry and the rest of which are raisin. How many
groups of 2 blueberry muffins and 3 raisin muffins can be chosen from the box?
__________________________________________________________________________________________
Target Goal: Find the probability of an event and determine the odds of success or failure..
Ex 1: There are 5 frozen juice bars and 8 frozen yogurt bars in the freezer. Dana reaches in the freezer and
grabs 2 without looking. Find the probability that she selects 2 juice bars.
Explain the following terms:
Success – desired outcome
Failure – any other outcome
Probability of success is as follows:
Answer to example 1:
Ex 2: What is the probability that she doesn’t grab 2 juice bars?
Probability of failure is as follows:
Answer to example 2:
Ex 3: Find the odds that she selects 2 juice bars.
Odds – ratio of successes to failures:
Answer to example 3:
Practice:
1. State the odds given a probability of
5
.
8
2. State the probability given odds of
6
.
5
3. The odds are 6 to 1 that our team will win on Friday. What is the probability that we will win?
4. A bag contains 6 white, 3 blue, and 7 green marbles. If one marble is chosen at random, what is the
probability of the following events?
a. marble is white
b. marble is not green
5. Three animals are to be chosen from a group of 3 bears, 6 tigers, and 4 lions. Find the probability of each
selection:
a. 1 bear, 1 tiger, and 1 lion
b. 3 bears
6. Suppose three letters are selected from the word ARRANGEMENTS. Find the odds of selecting 3
consonants.
7. Find the probability and the odds of the following events if two distinguishable dice are tossed.
a. dice total 7
b. at least one 2 appears
Assignment #4: Worksheet
Honors Advanced Algebra with Trigonometry
Probability
Assignment #4
Name: _____________________
Date: ______________________
Period: ____________________
State the odds of an event occurring given the probability of the event.
1.
1
7
2.
7
15
State the probability of an event occurring given the odds of the event.
3.
5
1
4.
1
1
Solve each problem.
5. The odds are 6-to-1 that the crosstown rivals will win in the championship football game on Friday night.
What is the probability that they will win?
6. The probability of Kelly getting an A on her final exam is
3
. What are the odds that she
4
will not get an A?
A canister contains 20 pieces of candy: 5 strawberry flavored, 9 watermelon flavored, and 6 mint
flavored. Two are selected at random. Find each probability.
7. P (2 watermelon)
8. P (1 strawberry and 1 mint)
There are 5 frozen juice bars and 8 frozen yogurt bars in the freezer. Dana reaches in a grabs 2 without
looking. Find the probability of each selection. Then find the odds of that selection.
9. P (2 yogurt bars)
10. P (1 of each kind)
Tommie’s bank contains 7 pennies, 4 nickels, and 5 dimes. His parents tell him that he can spend the
first three coins that he can shake out of the bank. Find each probability.
11. P(all pennies)
12. P (1 dime, 2 nickels)
13. P (1 dime, 1 nickel, 1 penny)
Suppose you select 2 letters at random from the word algebra. Find each probability.
14. P (selecting 2 consonants)
15. P (selecting 2 vowels)
16. P (selecting 1 vowel and 1 consonant)
From a deck of 52 playing cards, 5 cards are dealt. What are the odds of each event occurring?
17. all aces
18. all face cards
Honors Advanced Algebra with Trigonometry
Multiplying Probabilities
Probability Notes (Day 5)
Name: _____________________
Date: ______________________
Period: ____________________
Warm-Up:
1. You must choose a code name for your grades to be posted. The code name must begin with a letter (not o),
then have any letter for two spaces (may repeat), and finally end in a digit. How many possible code names
are there?
2. Determine which is a permutation or combination and then solve for each of the following.
a. How many ways can a team of 5 be chosen from a roster of 12?
b. How many ways can a team of 5 be introduced for a game from a roster of 12?
c. Out of 8 books, how many different orders are there to read 3 books?
d. Out of 8 books, how many different groups of 3 books exist?
3. A bag contains 6 white, 3 blue, and 7 green marbles. If one marble is chosen at random, what is the
probability that the marble is blue? What are the odds that the marble is blue?
4. Four animals are to be chosen from a group of 2 bears, 5 tigers, and 3 lions. Find the probability that 1 bear,
1 tiger, and 2 lions are selected. What are the odds for this selection?
__________________________________________________________________________________________
Target Goal: Find the probability of two or more independent or dependent events..
Note: None of the problems that follow refer to lining up items in any sort of order, and thus we will not be
using permutations in any way. We can either consider straight fractions, or use combinations if
preferred.
Independent – when the outcome of the 1st selection does not affect the outcome of the 2nd selection
Probability of two independent events – if two events, A and B, are independent, then the probability of both
events occurring is found as follows:
Ex 1: You spin the spinner 4 times. Find the probability that you get B, then C, then B, then A.
B
A
A
C
B
A
Dependent – when the outcome of the 1st selection does affect the outcome of the 2nd selection
Probability of two dependent events – if two events, A and B, are dependent, then the probability of both events
occurring is found as follows:
Ex 2: There are 3 quarters, 4 dimes, and 5 nickels in a purse. Suppose 3 coins are to be selected without
replacement. Find the following probabilities:
a. selecting 3 quarters
b. selecting a quarter, then a dime, then a nickel
Practice:
1. A bag contains 6 orange, 8 blue, and 4 yellow marbles. What is the probability of selecting 2 blue marbles
in succession provided the following:
a. the marble drawn first is then replaced before the second is drawn?
b. the marble drawn first is not replaced before the second is drawn?
2. A green, a red, and a blue die are tossed. Find each probability:
a. only the green die has a 5
b. all three dice have different numbers
3. Christine helps her dad do the dishes. There are 5 bowls, 3 glasses, and 8 plates sitting ready to be
washed. She accidentally knocks two items off the counter and breaks them. What is the probability that
she broke 2 bowls?
4. In the problem above, if Christine broke the items at different times, what is the probability that she first
broke a bowl and then broke one of the glasses?
Assignment #5: Worksheet
Honors Advanced Algebra with Trigonometry
Multiplying Probabilities
Assignment #5
Name: _____________________
Date: ______________________
Period: ____________________
Determine if each event is independent or dependent. Then find the probability.
1. There are 4 glasses of iced tea and 3 glasses of lemonade on the counter. Bill drinks two of them at random.
What is the probability that he drank 2 glasses of iced tea?
2. Monique came home from school to find a bowl of 5 apricots and 4 plums on the table. She decides to have
a snack. First she selects one then puts it back. She then selects another. What is the probability both
selections were apricots?
3. When Josh plays Sven on his video game, the odds are 3 to 2 that he will win. What is the probability that
he will win the next four games?
The Scrabble tiles A, B, E, I, J, K, and M are placed face down in the lid of the game and mixed up. Two
tiles are chosen at random. Find each probability.
4. P (selecting 2 vowels), if no replacement occurs
5. P (selecting 2 vowels), if replacement occurs
6. P (selecting the same letter twice), if no replacement occurs
Christine helps her dad do the dishes. There are 5 bowls, 5 glasses, and 6 plates sitting ready to be
washed. She accidentally knocks two items off the counter and breaks them. Find each probability.
7. P (breaking 2 plates)
8. P (breaking a bowl, then a glass)
Two dice are tossed. Find each probability.
9.
P (two 3s)
10. P (3 and then 4)
11. P (2 numbers alike)
12. A jar contains 5 peanut butter cookies, 3 caramel delights, and 7 lemon cookies. If 3 cookies are selected in
succession (p then c then l), find the probability of selecting one of each if:
a. no cookies are replaced
b. each cookie is replaced
13. Students in Geometry class are practicing constructions. The classroom toolbox contains 20 compasses as
follows: 12 of them have red pencils, 5 have blue pencils, and 3 have yellow pencils. Find the probability
of picking two compasses, one with a yellow pencil and then one with a red pencil. None of the compasses
are put back in the box.
Honors Advanced Algebra with Trigonometry
Adding Probabilities
Probability Notes (Day 6)
Name: _____________________
Date: ______________________
Period: ____________________
Warm-Up:
1. Write the sample space for the genders of three children in a family.
2. Christine helps her dad do the dishes. There are 6 bowls, 3 glasses, and 8 plates sitting ready to be washed.
She accidentally knocks two items off the counter and breaks them. What is the probability that she broke a
bowl and a glass?
3. In the problem above, if Christine broke the items at different times, what is the probability that she first
broke a bowl and then broke a glass?
4. In the problem above, what is the probability that Christine broke 2 plates?
__________________________________________________________________________________________
Target Goal: Find the probability of mutually exclusive events or inclusive events..
Recall: “and” we ______________, “or” we ______________. Yesterday, we worked with problems that
asked for the probability of one thing AND another, thus we multiplied. Today we are being asked for the
probability of one thing OR another, and thus we will add!
Ex 1: Suppose a card is drawn from a standard deck, what is the probability of drawing an ace or a queen?
We call drawing an ace or a queen mutually exclusive events because they are two events that cannot occur at
the same time.
Ex 2: Suppose a card is drawn from a standard deck, what is the probability of drawing an ace or a red card?
We call drawing an ace or a red card inclusive events because they are two events that can occur at
the same time, that is, there are some aces that are also red cards.
For both mutually exclusive and inclusive events, we calculate the sum of the probabilities of both events
occurring separately and then subtract the probability of both occurring together. For mutually exclusive
events, the probability of both occurring together is always zero.
Complete example 1 from the first side:
Suppose a card is drawn from a standard deck, what is the probability of drawing an ace or a queen?
Complete example 2 from the first side:
Suppose a card is drawn from a standard deck, what is the probability of drawing an ace or a red card?
Practice:
1. Two cards are drawn from a standard deck of 52 cards. What is the probability of the following:
a. 2 spades
b. 2 red cards or 2 jacks
2. A letter is picked at random from the alphabet. What is the probability the letter is contained in the word
GLASS or in the word SLOWER?
3. A bag contains 7 white and 5 blue marbles. Four marbles are selected without replacement. What is the
probability of the following:
a. all are white or all are blue
b. exactly three are white
c. at least three are white
Assignment #6: Worksheet
Honors Advanced Algebra with Trigonometry
Adding Probabilities
Assignment #6
Name: _____________________
Date: ______________________
Period: ____________________
Determine if each event is inclusive or mutually exclusive. Then find the probability.
1. Mrs. Martell has 15 photos of relatives in her wallet. Five are pictures of her children, 3 are pictures of her
sisters, and 7 are pictures of her grandchildren. She selects three photos at random. What is the probability
that she has selected 3 photos of her children or 3 photos of her grandchildren?
2. In homeroom, 3 of the 16 girls have red hair and 2 of the 15 boys have red hair. What is the probability of
selecting a boy or a red-haired person as homeroom representative to student council?
Ken has 11 coasters in a kitchen drawer. Six are cork and 5 are plastic. He selects three at random to
use in the family room. Find each probability.
3. P (all 3 cork or all 3 plastic)
4. P (at least 2 plastic)
Two cards are drawn from a deck of cards. Find each probability.
5. P (both black or both face cards)
6. P (both aces or both red)
Six men and 8 women arrive at the same time at a no-appointment-needed hair salon. There are six
stylists waiting to serve them. Find the probability of each group of six being served first.
7. P (all men or all women)
8. P (4 men or 4 women)
Honors Advanced Algebra with Trigonometry
Probability Review
Assignment #7
Name: _____________________
Date: ______________________
Period: ____________________
Solve each problem.
1. Using the digits 0, 1, 2, 3, and 4, how many 3-digit patterns can be formed if the numbers can be used more
than once?
2. Using the digits 5, 6, 7, 8, and 9, how many 3-digit patterns can be formed if each number can only be used
once?
On a shelf are 8 mystery and 7 romance novels. How many ways can they be arranged for each
situation?
3. all mysteries together
4. all mysteries together, all romances together
Solve each problem.
5. Three players on a baseball team are only permitted to pitch. The remaining 12 players are multitalented
and can play any of the 8 remaining positions. How many baseball teams of nine can be formed?
6. From a deck of 52 cards, how many different 4-card hands exist?
7. A card is selected from a deck of 52 cards. What is the probability that it is a queen? What are the odds?
8. A bag of marbles contains 6 red and 2 white marbles. If two marbles are selected, what is the probability
that one is red and the other is white?
9. In his pocket, Jose has 5 dimes, 7 nickels, and 4 pennies. He selects 4 coins. What is the probability that he
has 2 dimes and 2 pennies?
10. Ben has 6 blue socks and 4 black socks in a drawer. One dark morning he pulls out 2 socks. What is the
probability that he has 2 black socks?
11. From a deck of 52 cards, one card is selected. What is the probability that it is an ace or a face card?
12. If a letter is selected at random from the alphabet, what is the probability that it is a letter from the words
CAT or SKATE?